Last updated at Aug. 23, 2021 by Teachoo

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Ex 10.2, 11 (Method 1) Show that the vectors 2๐ ฬ โ 3๐ ฬ + 4๐ ฬ and โ 4๐ ฬ + 6 ๐ ฬ โ 8๐ ฬ are collinear.Two vectors are collinear if they are parallel to the same line. Let ๐ โ = 2๐ ฬ โ 3๐ ฬ + 4๐ ฬ and ๐ โ = โ4๐ ฬ + 6๐ ฬ โ 8๐ ฬ Magnitude of ๐ โ = โ(22+(โ3)2+42) |๐ โ | = โ(4+9+16) = โ29 Directions cosines of ๐ โ = (2/โ29,(โ3)/โ29,4/โ29) Magnitude of ๐ โ =โ((โ4)2+62+(โ8)2) |๐ โ | = โ(16+36+64) = โ116 = 2โ29 Directions cosines of ๐ โ = ((โ4)/(2โ29),6/(2โ29),(โ8)/(2โ29)) = ((โ2)/โ29,3/โ29,(โ4)/โ29) = โ1(2/โ29,(โ3)/โ29,4/โ29) Hence, Direction cosines of ๐ โ = (โ1) ร Direction cosines of ๐ โ โด They have opposite directions Since ๐ โ and ๐ โ are parallel to the same line ๐ โ, they are collinear. Hence proved Ex 10.2, 11 (Method 2) Show that the vectors 2๐ ฬ โ 3๐ ฬ + 4๐ ฬ and โ 4๐ ฬ + 6 ๐ ฬ โ 8๐ ฬ are collinear.๐ โ = 2๐ ฬ โ 3๐ ฬ + 4๐ ฬ ๐ โ = โ4๐ ฬ + 6๐ ฬ โ 8๐ ฬ Two vectors are collinear if their directions ratios are proportional ๐_1/๐_1 = ๐_2/๐_2 = ๐_3/๐_3 = ๐ 2/(โ4) = (โ3)/6 = 4/(โ8) = (โ1)/2 Since, directions ratios are proportional Hence, ๐ โ & ๐ โ are collinear

Ex 10.2

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Ex 10.2, 11 Important You are here

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Ex 10.2, 18 (MCQ) Important

Ex 10.2, 19 (MCQ) Important

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.